Standard and Vertex Forms

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does the 'a' in the quadratic equation y = ax² + bx + c represent?

Back

The 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

How can you identify the vertex of a parabola from its vertex form?

Back

In the vertex form y = a(x - h)² + k, the vertex is the point (h, k).

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, which is a U-shaped curve that can open upwards or downwards.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = h in vertex form.

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form y = ax² + bx + c to vertex form, you can complete the square.

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards when the coefficient 'a' in the equation y = ax² + bx + c is positive.

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards when the coefficient 'a' in the equation y = ax² + bx + c is negative.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on whether it opens upwards or downwards.